The building blocks of the Sharpe ratio—expected returns and volatilities—are unknown quantities that must be estimated statistically and are subject to estimation error.
The main problem I have is how to compute the return. Simple return or Log-return? As it concerns financial returns, I am personally think log-returns, but this dampens the volatility.
I am using a weekly return index (with dividend reinvestment) of Asian REITs. Reason for this that if I use daily, there are some 'missing' values due to holiday or non trading days that differ per Asian country. I've seen other researchers use the same method (Ooi et al. 2006). I suppose to annualize this data I have to multiply the average return by $\sqrt{52}$. But should I use geometric or arithmetic means?
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